TSTP Solution File: KRS112+1 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:43:22 EDT 2023
% Result : Unsatisfiable 7.29s 7.46s
% Output : Proof 7.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KRS112+1 : TPTP v8.1.2. Released v3.1.0.
% 0.06/0.12 % Command : duper %s
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Mon Aug 28 01:18:12 EDT 2023
% 0.11/0.33 % CPUTime :
% 7.29/7.46 SZS status Theorem for theBenchmark.p
% 7.29/7.46 SZS output start Proof for theBenchmark.p
% 7.29/7.46 Clause #25 (by assumption #[]): Eq
% 7.29/7.46 (∀ (X : Iota),
% 7.29/7.46 Iff (cUnsatisfiable X) (And (Exists fun Y => And (rf1 X Y) (ca_Ax2 Y)) (Exists fun Y => And (rf X Y) (cp Y))))
% 7.29/7.46 True
% 7.29/7.46 Clause #26 (by assumption #[]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists fun Y => ra_Px1 X Y))) True
% 7.29/7.46 Clause #27 (by assumption #[]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists fun Y0 => ra_Px1 X Y0)) True
% 7.29/7.46 Clause #28 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Ax2 X) (And (cpxcomp X) (∀ (Y : Iota), rinvF1 X Y → ca_Vx3 Y))) True
% 7.29/7.46 Clause #29 (by assumption #[]): Eq (∀ (X : Iota), Iff (ca_Vx3 X) (Exists fun Y => And (rs X Y) (cowlThing Y))) True
% 7.29/7.46 Clause #30 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf X Y) (rf X Z) → Eq Y Z) True
% 7.29/7.46 Clause #31 (by assumption #[]): Eq (∀ (X Y Z : Iota), And (rf1 X Y) (rf1 X Z) → Eq Y Z) True
% 7.29/7.46 Clause #33 (by assumption #[]): Eq (∀ (X Y : Iota), Iff (rinvF1 X Y) (rf1 Y X)) True
% 7.29/7.46 Clause #36 (by assumption #[]): Eq (cUnsatisfiable i2003_11_14_17_21_19256) True
% 7.29/7.46 Clause #37 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf X Y) True
% 7.29/7.46 Clause #38 (by assumption #[]): Eq (∀ (X Y : Iota), rs X Y → rf1 X Y) True
% 7.29/7.46 Clause #93 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf a Y) True
% 7.29/7.46 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf a a_1) True
% 7.29/7.46 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf a a_1) True)
% 7.29/7.46 Clause #103 (by clausification #[38]): ∀ (a : Iota), Eq (∀ (Y : Iota), rs a Y → rf1 a Y) True
% 7.29/7.46 Clause #104 (by clausification #[103]): ∀ (a a_1 : Iota), Eq (rs a a_1 → rf1 a a_1) True
% 7.29/7.46 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Or (Eq (rs a a_1) False) (Eq (rf1 a a_1) True)
% 7.29/7.46 Clause #205 (by clausification #[31]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf1 a Y) (rf1 a Z) → Eq Y Z) True
% 7.29/7.46 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf1 a a_1) (rf1 a Z) → Eq a_1 Z) True
% 7.29/7.46 Clause #207 (by clausification #[206]): ∀ (a a_1 a_2 : Iota), Eq (And (rf1 a a_1) (rf1 a a_2) → Eq a_1 a_2) True
% 7.29/7.46 Clause #208 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf1 a a_1) (rf1 a a_2)) False) (Eq (Eq a_1 a_2) True)
% 7.29/7.46 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf1 a_2 a) False) (Eq (rf1 a_2 a_1) False))
% 7.29/7.46 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf1 a a_1) False) (Or (Eq (rf1 a a_2) False) (Eq a_1 a_2))
% 7.29/7.46 Clause #211 (by clausification #[30]): ∀ (a : Iota), Eq (∀ (Y Z : Iota), And (rf a Y) (rf a Z) → Eq Y Z) True
% 7.29/7.46 Clause #212 (by clausification #[211]): ∀ (a a_1 : Iota), Eq (∀ (Z : Iota), And (rf a a_1) (rf a Z) → Eq a_1 Z) True
% 7.29/7.46 Clause #213 (by clausification #[212]): ∀ (a a_1 a_2 : Iota), Eq (And (rf a a_1) (rf a a_2) → Eq a_1 a_2) True
% 7.29/7.46 Clause #214 (by clausification #[213]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (rf a a_1) (rf a a_2)) False) (Eq (Eq a_1 a_2) True)
% 7.29/7.46 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 : Iota), Or (Eq (Eq a a_1) True) (Or (Eq (rf a_2 a) False) (Eq (rf a_2 a_1) False))
% 7.29/7.46 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 : Iota), Or (Eq (rf a a_1) False) (Or (Eq (rf a a_2) False) (Eq a_1 a_2))
% 7.29/7.46 Clause #217 (by clausification #[33]): ∀ (a : Iota), Eq (∀ (Y : Iota), Iff (rinvF1 a Y) (rf1 Y a)) True
% 7.29/7.46 Clause #218 (by clausification #[217]): ∀ (a a_1 : Iota), Eq (Iff (rinvF1 a a_1) (rf1 a_1 a)) True
% 7.29/7.46 Clause #219 (by clausification #[218]): ∀ (a a_1 : Iota), Or (Eq (rinvF1 a a_1) True) (Eq (rf1 a_1 a) False)
% 7.29/7.46 Clause #221 (by clausification #[25]): ∀ (a : Iota),
% 7.29/7.46 Eq (Iff (cUnsatisfiable a) (And (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) (Exists fun Y => And (rf a Y) (cp Y))))
% 7.29/7.46 True
% 7.29/7.46 Clause #223 (by clausification #[221]): ∀ (a : Iota),
% 7.29/7.46 Or (Eq (cUnsatisfiable a) False)
% 7.29/7.46 (Eq (And (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) (Exists fun Y => And (rf a Y) (cp Y))) True)
% 7.29/7.46 Clause #237 (by betaEtaReduce #[27]): Eq (∀ (X : Iota), Iff (cpxcomp X) (Exists (ra_Px1 X))) True
% 7.29/7.50 Clause #238 (by clausification #[237]): ∀ (a : Iota), Eq (Iff (cpxcomp a) (Exists (ra_Px1 a))) True
% 7.29/7.50 Clause #240 (by clausification #[238]): ∀ (a : Iota), Or (Eq (cpxcomp a) False) (Eq (Exists (ra_Px1 a)) True)
% 7.29/7.50 Clause #242 (by betaEtaReduce #[26]): Eq (∀ (X : Iota), Iff (cp X) (Not (Exists (ra_Px1 X)))) True
% 7.29/7.50 Clause #243 (by clausification #[242]): ∀ (a : Iota), Eq (Iff (cp a) (Not (Exists (ra_Px1 a)))) True
% 7.29/7.50 Clause #245 (by clausification #[243]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Not (Exists (ra_Px1 a))) True)
% 7.29/7.50 Clause #250 (by clausification #[240]): ∀ (a a_1 : Iota), Or (Eq (cpxcomp a) False) (Eq (ra_Px1 a (skS.0 1 a a_1)) True)
% 7.29/7.50 Clause #252 (by clausification #[245]): ∀ (a : Iota), Or (Eq (cp a) False) (Eq (Exists (ra_Px1 a)) False)
% 7.29/7.50 Clause #253 (by clausification #[252]): ∀ (a a_1 : Iota), Or (Eq (cp a) False) (Eq (ra_Px1 a a_1) False)
% 7.29/7.50 Clause #254 (by clausification #[28]): ∀ (a : Iota), Eq (Iff (ca_Ax2 a) (And (cpxcomp a) (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y))) True
% 7.29/7.50 Clause #256 (by clausification #[254]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (And (cpxcomp a) (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y)) True)
% 7.29/7.50 Clause #263 (by clausification #[256]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (∀ (Y : Iota), rinvF1 a Y → ca_Vx3 Y) True)
% 7.29/7.50 Clause #264 (by clausification #[256]): ∀ (a : Iota), Or (Eq (ca_Ax2 a) False) (Eq (cpxcomp a) True)
% 7.29/7.50 Clause #265 (by clausification #[263]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Eq (rinvF1 a a_1 → ca_Vx3 a_1) True)
% 7.29/7.50 Clause #266 (by clausification #[265]): ∀ (a a_1 : Iota), Or (Eq (ca_Ax2 a) False) (Or (Eq (rinvF1 a a_1) False) (Eq (ca_Vx3 a_1) True))
% 7.29/7.50 Clause #267 (by clausification #[29]): ∀ (a : Iota), Eq (Iff (ca_Vx3 a) (Exists fun Y => And (rs a Y) (cowlThing Y))) True
% 7.29/7.50 Clause #269 (by clausification #[267]): ∀ (a : Iota), Or (Eq (ca_Vx3 a) False) (Eq (Exists fun Y => And (rs a Y) (cowlThing Y)) True)
% 7.29/7.50 Clause #274 (by clausification #[269]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (And (rs a (skS.0 3 a a_1)) (cowlThing (skS.0 3 a a_1))) True)
% 7.29/7.50 Clause #276 (by clausification #[274]): ∀ (a a_1 : Iota), Or (Eq (ca_Vx3 a) False) (Eq (rs a (skS.0 3 a a_1)) True)
% 7.29/7.50 Clause #279 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf a Y) (cp Y)) True)
% 7.29/7.50 Clause #280 (by clausification #[223]): ∀ (a : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (Exists fun Y => And (rf1 a Y) (ca_Ax2 Y)) True)
% 7.29/7.50 Clause #281 (by clausification #[279]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf a (skS.0 4 a a_1)) (cp (skS.0 4 a a_1))) True)
% 7.29/7.50 Clause #282 (by clausification #[281]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (cp (skS.0 4 a a_1)) True)
% 7.29/7.50 Clause #283 (by clausification #[281]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf a (skS.0 4 a a_1)) True)
% 7.29/7.50 Clause #284 (by superposition #[282, 36]): ∀ (a : Iota), Or (Eq (cp (skS.0 4 i2003_11_14_17_21_19256 a)) True) (Eq False True)
% 7.29/7.50 Clause #285 (by clausification #[284]): ∀ (a : Iota), Eq (cp (skS.0 4 i2003_11_14_17_21_19256 a)) True
% 7.29/7.50 Clause #286 (by superposition #[285, 253]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_19256 a) a_1) False)
% 7.29/7.50 Clause #287 (by clausification #[280]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (And (rf1 a (skS.0 5 a a_1)) (ca_Ax2 (skS.0 5 a a_1))) True)
% 7.29/7.50 Clause #288 (by clausification #[287]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (ca_Ax2 (skS.0 5 a a_1)) True)
% 7.29/7.50 Clause #289 (by clausification #[287]): ∀ (a a_1 : Iota), Or (Eq (cUnsatisfiable a) False) (Eq (rf1 a (skS.0 5 a a_1)) True)
% 7.29/7.50 Clause #290 (by superposition #[288, 36]): ∀ (a : Iota), Or (Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_19256 a)) True) (Eq False True)
% 7.29/7.50 Clause #291 (by clausification #[290]): ∀ (a : Iota), Eq (ca_Ax2 (skS.0 5 i2003_11_14_17_21_19256 a)) True
% 7.29/7.50 Clause #292 (by superposition #[291, 266]): ∀ (a a_1 : Iota),
% 7.29/7.50 Or (Eq True False) (Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False) (Eq (ca_Vx3 a_1) True))
% 7.37/7.54 Clause #293 (by superposition #[291, 264]): ∀ (a : Iota), Or (Eq True False) (Eq (cpxcomp (skS.0 5 i2003_11_14_17_21_19256 a)) True)
% 7.37/7.54 Clause #294 (by clausification #[293]): ∀ (a : Iota), Eq (cpxcomp (skS.0 5 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #295 (by superposition #[294, 250]): ∀ (a a_1 : Iota),
% 7.37/7.54 Or (Eq True False)
% 7.37/7.54 (Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1)) True)
% 7.37/7.54 Clause #298 (by clausification #[286]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 4 i2003_11_14_17_21_19256 a) a_1) False
% 7.37/7.54 Clause #302 (by superposition #[289, 36]): ∀ (a : Iota), Or (Eq (rf1 i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True) (Eq False True)
% 7.37/7.54 Clause #303 (by clausification #[302]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #304 (by superposition #[303, 210]): ∀ (a a_1 : Iota),
% 7.37/7.54 Or (Eq True False) (Or (Eq (rf1 i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a))
% 7.37/7.54 Clause #305 (by superposition #[303, 219]): ∀ (a : Iota), Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) i2003_11_14_17_21_19256) True) (Eq True False)
% 7.37/7.54 Clause #307 (by clausification #[305]): ∀ (a : Iota), Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) i2003_11_14_17_21_19256) True
% 7.37/7.54 Clause #310 (by superposition #[283, 36]): ∀ (a : Iota), Or (Eq (rf i2003_11_14_17_21_19256 (skS.0 4 i2003_11_14_17_21_19256 a)) True) (Eq False True)
% 7.37/7.54 Clause #311 (by clausification #[310]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 4 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #316 (by clausification #[304]): ∀ (a a_1 : Iota), Or (Eq (rf1 i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a)
% 7.37/7.54 Clause #318 (by clausification #[292]): ∀ (a a_1 : Iota), Or (Eq (rinvF1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False) (Eq (ca_Vx3 a_1) True)
% 7.37/7.54 Clause #319 (by superposition #[318, 307]): Or (Eq (ca_Vx3 i2003_11_14_17_21_19256) True) (Eq False True)
% 7.37/7.54 Clause #321 (by clausification #[319]): Eq (ca_Vx3 i2003_11_14_17_21_19256) True
% 7.37/7.54 Clause #322 (by superposition #[321, 276]): ∀ (a : Iota), Or (Eq True False) (Eq (rs i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True)
% 7.37/7.54 Clause #323 (by clausification #[322]): ∀ (a : Iota), Eq (rs i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #324 (by superposition #[323, 95]): ∀ (a : Iota), Or (Eq True False) (Eq (rf i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True)
% 7.37/7.54 Clause #325 (by superposition #[323, 105]): ∀ (a : Iota), Or (Eq True False) (Eq (rf1 i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True)
% 7.37/7.54 Clause #330 (by clausification #[325]): ∀ (a : Iota), Eq (rf1 i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #331 (by superposition #[330, 316]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 3 i2003_11_14_17_21_19256 a_1))
% 7.37/7.54 Clause #335 (by clausification #[295]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1)) True
% 7.37/7.54 Clause #338 (by clausification #[324]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 3 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #354 (by clausification #[331]): ∀ (a a_1 : Iota), Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 3 i2003_11_14_17_21_19256 a_1)
% 7.37/7.54 Clause #363 (by superposition #[354, 338]): ∀ (a : Iota), Eq (rf i2003_11_14_17_21_19256 (skS.0 5 i2003_11_14_17_21_19256 a)) True
% 7.37/7.54 Clause #377 (by superposition #[363, 216]): ∀ (a a_1 : Iota),
% 7.37/7.54 Or (Eq True False) (Or (Eq (rf i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a))
% 7.37/7.54 Clause #387 (by clausification #[377]): ∀ (a a_1 : Iota), Or (Eq (rf i2003_11_14_17_21_19256 a) False) (Eq (skS.0 5 i2003_11_14_17_21_19256 a_1) a)
% 7.37/7.54 Clause #388 (by superposition #[387, 311]): ∀ (a a_1 : Iota), Or (Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 4 i2003_11_14_17_21_19256 a_1)) (Eq False True)
% 7.37/7.54 Clause #393 (by clausification #[388]): ∀ (a a_1 : Iota), Eq (skS.0 5 i2003_11_14_17_21_19256 a) (skS.0 4 i2003_11_14_17_21_19256 a_1)
% 7.37/7.54 Clause #405 (by superposition #[393, 298]): ∀ (a a_1 : Iota), Eq (ra_Px1 (skS.0 5 i2003_11_14_17_21_19256 a) a_1) False
% 7.37/7.54 Clause #427 (by superposition #[405, 335]): Eq False True
% 7.37/7.54 Clause #430 (by clausification #[427]): False
% 7.37/7.54 SZS output end Proof for theBenchmark.p
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